Pre-Algebra Trimester 3 Study Guide
1. State whether each graph is a function. Write yes or no next to each graph. Explain why
or why not.
2. Determine whether the following relations are a function. Explain why or why not. State the
domain and range of the following set of data:
a)
b) {(-4, 3), (7, 2), (2, -6), (8, -5)}
c)
x
y
-6
-2
-4
-1
-3
1
3
3
5
8
GRAPHING
Complete the function table. Graph the line.
3.
1
𝑥
2
x
1
𝑥+3=𝑦
2
x
𝑦 = 3𝑥 − 4
y
(x,y)
x
2𝑥 + 𝑦 = 4
Y
(x,y)
+3=𝑦
y
4.
𝑦 = 3𝑥 − 4
5. 2x + y = 4
(x,y)
6.
x= 3
x
𝑥=3
GRAPH using X and Y intercepts.
7. -4x + 2y = 8
9.
3x – 6y = -12
8. y = -2x + 4
10. Y = -2
y
(x,y)
Graph using slope and y- intercept.
11) y = -3/4x + 2
12) y = 3x
13. 2x + y = -5
14. Y = -3
Find the slope of each.
15. (-3, -1) and (-2, -2)
16. (4, 3) and (-2, 6)
17. (5, -3) and (5, -2)
18. (12, 4) and (-8, 4)
19.
20.
WRITING LINEAR EQAUTIONS
Write a linear equation in slope-intercept form with the given information.
21) m= 6
b = -4
22) slope = ½
23) (-2, 3) m = 1
24) (5, 10) m = 3
25) (3,3) (7, -1)
26) (1.5) (2,8)
27)
b=4
28)
x
y
x
y
-1
5
-1
9
0
10
0
6
1
15
1
3
2
20
2
0
29) Dillon has 52 baseball cards in his collection. He adds about 10 cards per year. Write a linear
equation where y is the total amount of cards Dillon has after x amount of years.
Geometry
Use the Pythagorean theorem to find the missing side of each right triangle.
30) a = ? b= 4 c = 5
31) a = 15 b = 17 c = ?
Determine whether the following lengths can be the measures of a right triangle.
32) 9 in, 12 in, 15 in
33) a= 6cm, b = 10 cm, c = 25 cm
Use an NJASK reference sheet to solve the following problems. Write down a formula, plug in, and
solve.
34) If the area of a circle is 100.48 sq. in., then what is the radius of the circle? What is the
circumference of the circle? (Use 3.14 for 𝜋) Label your answers!
35)Find the volume of a cone whose radius is 10 feet and height is 15 feet.
36)Find the surface area of a sphere whose radius is 8 cm.
37)Find the height of a cone whose radius is 15 feet and volume is 330 cubic feet.
38)What is the sum of the measures of the interior angles of a regular …….
a) heptagon
b) nonagon
c) hexagon
39)What is the measure of one of the interior angle in a regular……..
a) pentagon
b) octagon
c) decagon
40)If the measures of the interior angles in a triangle are x°, 2x° and 6x°, find x. Is this an acute,
obtuse or right triangle?
41)∠𝐺 𝑎𝑛𝑑 ∠𝐻 are complementary angles. ∠G is 35°. What is the measure of ∠𝐻?
42) ∠𝐺 𝑎𝑛𝑑 ∠𝐻 are supplementary angles. ∠G is 35°. What is the measure of ∠𝐻?
43) Find the value of x and/or y. Find the missing angles.
110°
y°
x°
(4x + 10) °
x°
Tell whether the situation is a permutation or combination. Then solve. Show all your
work.
43) How many ways can 7 horses line up for a race?
44) How many ways can 22 students be arranged in a 4 student line?
45) How many ways can a 3 person tennis team be chosen from 10 students?
46) There are 12 students participating in a spelling bee. How many ways can the students be
chosen to go first, second, third, and fourth?
47) Jessie wants to make a bouquet that contains 5 flowers. If she has a choice of 10 flowers,
how many different bouquets can be made?
Find the missing angle measures. Figures are not drawn to scale.
48.
49.
37°
48°
50.
126°
x°
x°
133°
72°
2x°
4x°
51.
y°
(2x + 4)°
83°
2x°
x°
140°
(x + 3)°
2x°
52. Find the missing angle measures. 𝑙 ∥ 𝑚 ∠1 = 125°
∠1
∠2
𝑙
∠3
∠5
∠4
∠6
𝑚
∠7
∠8
∠2_________ ∠3_________ ∠4_________ ∠5_________ ∠6_________ ∠7________ ∠8_________
Find the length of the missing sides, X, Y and Z. Figures are similar, but not drawn to scale.
SHOW ALL WORK! Be sure to label your answer.
53.
18 cm
12 cm
X cm
15 cm
54.
65 in
48.75 in
27 in
Y in
55.
Z ft
5.8 ft
1.2 ft
8.9 ft
Solve each system of equations by graphing. Label your graph. Write your answer as an ordered
pair.
56. 𝑦 = −𝑥
57. 𝑦 = 𝑥 + 1
𝑦=𝑥−4
𝑥+𝑦 =7
Solve each system of equations using substitution. Show all work!
58. 𝑦 = 𝑥 + 2
59. 𝑦 = 𝑥 + 4
𝑥=1
𝑦=0
60. Amanda pays an annual fee of $100 to belong to a gym, plus a monthly fee of $10. Maria
pays only a monthly fee of $20.
a. Write a system of equations to represent this situation. Let y represent the total cost and x
represent the number of months.
b. Solve the system by graphing.
c. After how many months will Anna and Maria have paid the same amount to their gyms?